How to make glowing particles, with a solid glowing center
3 Concentric Spheres with Emission Particles

Blur in Compositor


Render result and 3 Concentric Spheres each with a particle system.  Image above.

Click on images to see larger view.



Compositor with Blur and Alpha Over Nodes. Image Above.


Particle Settings. 3 Panel of which 2 are pinned.  Unpinned is the largest sphere particle system.  Image above.



The 3 Object particles and the material settings. 2 are pinned.

Please experiment to your taste and improve.
Consider using a more irregular sphere in the center.
You may look at the movement of particle system on many frames and choose some particular frame.

Sloppy Imitation which may serve as a starting point.
Of course there are alternative and more CPU intensive ways to do this.